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Your 300mL cup of coffee is too hot to drink when served at 87C. What is the mass of an ice cube, taken from a -20C freezer, that will cool your coffee to a pleasant 58C?

  • physics - ,

    You want to remove M C (delta T) = 300 g*1.00 Cal/(g C) * 29 C = 8700 calories from the coffee. If m is the mass of ice you add, the heat absorbed by the ice while melting and incresing in temperature from -20 to +58 C is
    m*Cice*(20) + mCwater*58 + m*80 Cal/g

    The specific heat of ice, Cice = 0.51 Cal/g C

    8700 cal = 10.2 m + 58 m + 80 m = 148.2
    Solve for m

  • physics - ,

    q1 = heat to move ice from -20 to zero.
    q1 = mass ice x specific heat ice x (Tfinal-Tinitial). [Tf will be 0 and Ti will be -20 but watch that sign since it will change.

    q2 = heat to melt the ice.
    q2 = mass ice x heat fusion.

    q3 = heat to move ice from zero to 58.
    q3 = mass ice x specific heat water (its now a liquid) x (58-0).

    q4 = loss of heat to move 300 mL water from 87 to 58.
    q4 = mass water x specific heat water x (58-87).
    q1 + q2 + q3 + q4 = 0
    You have only one unknown in all of the above which is mass ice. Solve for that. Check my thinking. I won't be on for the next 6 hours or so.

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